论文标题
在存在部门约束的情况下的因果结构，并应用于量子开关
Causal structure in the presence of sectorial constraints, with application to the quantum switch
论文作者
论文摘要
量子因果结构上的现有工作假设可以对感兴趣的系统进行任意操作。但是这种情况通常无法满足。在这里，我们将量子因果建模的框架扩展到系统可能遭受部门约束的情况，即对其希尔伯特空间的正交子空间的限制，这些子空间可能彼此映射。我们的框架（a）证明，关于因果关系的许多不同直觉相同； （b）表明，在存在部门约束的情况下，量子因果结构可以用有向图表示； （c）定义了系统关系的各个部门带有因果关系的细粒。例如，我们将框架应用于声称量子开关的光子实现，以表明虽然它们的粗粒子因果结构是循环的，但它们的细粒度因果结构是无环的。因此，我们得出的结论是，这些实验仅在薄弱的意义上才实现无限期的因果秩序。值得注意的是，这是这种效应的第一个论点，该论点不是基于因果关系必须定位在时空中的假设。
Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a system can suffer sectorial constraints, that is, restrictions on the orthogonal subspaces of its Hilbert space that may be mapped to one another. Our framework (a) proves that a number of different intuitions about causal relations turn out to be equivalent; (b) shows that quantum causal structures in the presence of sectorial constraints can be represented with a directed graph; and (c) defines a fine-graining of the causal structure in which the individual sectors of a system bear causal relations. As an example, we apply our framework to purported photonic implementations of the quantum switch to show that while their coarse-grained causal structure is cyclic, their fine-grained causal structure is acyclic. We therefore conclude that these experiments realize indefinite causal order only in a weak sense. Notably, this is the first argument to this effect that is not rooted in the assumption that the causal relata must be localized in spacetime.
